import java.io.*;
import java.util.*;
import java.util.concurrent.CountDownLatch;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;

////////////////////////////////   Solve Sudoku Puzzles   ////////////////////////////////
////////////////////////////////   @author Peter Norvig   ////////////////////////////////
////////////////////////////////        2007, 2021        ////////////////////////////////

/** Solve Sudoku Puzzles
 ** @author Peter Norvig
 ** Mostly 2007, som2 2021, 2026
 **
 ** There are two representations of puzzles that we will use:
 **  1. A gridstring is 81 chars, with characters '0' or '.' for blank and '1' to '9' for digits.
 **  2. A puzzle grid is an int[81] with a digit d (1-9) represented by the integer (1 << (d - 1));
 **     that is, a bit pattern that has a single 1 bit representing the digit.
 **     A blank is represented by the OR of all the digits 1-9, meaning any digit is possible.
 **     While solving the puzzle, some of these digits are eliminated, leaving fewer possibilities.
 **     The puzzle is solved when every square has only a single possibility.
 **
 ** Search for a solution with `search`:
 **   - Fill an empty square with a guessed digit and do constraint propagation.
 **   - If the guess is consistent, search deeper; if not, try a different guess for the square.
 **   - If all guesses fail, back up to the previous level.
 **   - In selecting an empty square, we pick one that has the minimum number of possible digits.
 **   - To be able to back up, we need to keep the grid from the previous recursive level.
 **     But we only need to keep one grid for each level, so to save garbage collection,
 **     we pre-allocate one grid per level (there are 81 levels) in a `gridpool`.
 ** Do constraint propagation with `arcConsistent`, `dualConsistent`, and `nakedPairs`.
 **/

public class Sudoku {

    //////////////////////////////// main; command line options //////////////////////////////

    static final String USAGE = String.join("\n",
        "usage: java Sudoku -(no)[fghnprstuv] | -[RT]<number> | <filename> ...",
        "Options and filenames are processed left-to-right. Use '-no' to turn an option off\n",
        "E.g.: -v turns verify flag on, -nov turns it off. -R and -T require a number. The options:\n",
        "  -g(rid)     Print each puzzle grid and solution grid (default off)",
        "  -h(elp)     Print this usage message",
        "  -n(aked)    Run the naked pairs strategy (default on)",
        "  -p(uzzle)   Print summary stats for each puzzle (default off)",
        "  -r(everse)  Solve the reverse of each puzzle as well as each puzzle itself (default off)",
        "  -s(ummary)  Print per-file summary stats (default on)",
        "  -t(hread)   Print summary stats for each thread (default off)",
        "  -u(nitTest) Run a suite of unit tests (default off)",
        "  -v(erify)   Verify each solution is valid (default on)",
        "  -T<number>  Concurrently run <number> threads (default 25)",
        "  -R<number>  Repeat the solving of each puzzle <number> times (default 1)",
        "  <filename>  Solve all puzzles in filename, which has one puzzle per line");

    boolean printGrid        = false; // -g
    boolean runNakedPairs    = true;  // -n
    boolean printPuzzleStats = false; // -p
    boolean reversePuzzle    = false; // -r
    boolean printFileStats   = true;  // -s
    boolean printThreadStats = false; // -t
    boolean verifySolution   = true;  // -v
    int     nThreads         = 25;    // -T
    int     repeat           = 1;     // -R

    private final AtomicInteger backtracks = new AtomicInteger(0);
    private volatile boolean headerPrinted = false;

    /** Parse command line args and solve puzzles in files. **/
    public static void main(String[] args) throws IOException {
        Sudoku s = new Sudoku();
        for (String arg : args) {
            if (!arg.startsWith("-")) {
                s.solveFile(arg);
            } else {
                boolean value = !arg.startsWith("-no");
                switch (arg.charAt(value ? 1 : 3)) {
                    case 'g' -> s.printGrid        = value;
                    case 'h' -> System.out.println(USAGE);
                    case 'n' -> s.runNakedPairs    = value;
                    case 'p' -> s.printPuzzleStats = value;
                    case 'r' -> s.reversePuzzle    = value;
                    case 's' -> s.printFileStats   = value;
                    case 't' -> s.printThreadStats = value;
                    case 'u' -> s.runUnitTests();
                    case 'v' -> s.verifySolution   = value;
                    case 'T' -> s.nThreads = Integer.parseInt(arg.substring(2));
                    case 'R' -> s.repeat   = Integer.parseInt(arg.substring(2));
                    default  -> System.out.println("Unrecognized option: " + arg + "\n" + USAGE);
                }
            }
        }
    }


    //////////////////////////////// Handling Lists of Puzzles ////////////////////////////////

    /** Solve all the puzzles in a file. Report timing statistics. **/
    void solveFile(String filename) throws IOException {
        List<int[]> grids = readPuzzlesFromFile(filename);
        long startFileTime = System.nanoTime();
        if (nThreads == 1) {
            solveList(grids);
        } else {
            solveListThreaded(grids, nThreads);
        }
        if (printFileStats) printStats(grids.size() * repeat, startFileTime, filename);
    }


    /** Solve a list of puzzles in a single thread.
     ** repeat -R<number> times; print each puzzle's stats if -p; print grid if -g; verify if -v. **/
    void solveList(List<int[]> grids) {
        int[] puzzle    = new int[N * N];
        int[][] gridpool = new int[N * N][N * N];
        for (int g = 0; g < grids.size(); ++g) {
            int[] grid = grids.get(g);
            System.arraycopy(grid, 0, puzzle, 0, grid.length);
            for (int i = 0; i < repeat; ++i) {
                long startTime = printPuzzleStats ? System.nanoTime() : 0;
                int[] solution = initialize(grid);
                solution = search(solution, gridpool, 0);
                if (printPuzzleStats) {
                    printStats(1, startTime, "Puzzle " + (g + 1));
                }
                if (i == 0 && (printGrid || (verifySolution && !verify(solution, puzzle)))) {
                    printGrids("Puzzle " + (g + 1), grid, solution);
                }
            }
        }
    }


    /** Break a list of puzzles into nThreads sublists and solve each sublist in a separate thread. **/
    void solveListThreaded(List<int[]> grids, int nThreads) {
        try {
            final long startTime = System.nanoTime();
            int nGrids = grids.size();
            final CountDownLatch latch = new CountDownLatch(nThreads);
            int size = nGrids / nThreads;
            for (int c = 0; c < nThreads; ++c) {
                int end = (c == nThreads - 1) ? nGrids : (c + 1) * size;
                final List<int[]> sublist = grids.subList(c * size, end);
                new Thread(() -> {
                    solveList(sublist);
                    latch.countDown();
                    if (printThreadStats) {
                        printStats(repeat * sublist.size(), startTime, "Thread");
                    }
                }).start();
            }
            latch.await();
        } catch (InterruptedException e) {
            Thread.currentThread().interrupt();
            System.err.println("Solver thread was interrupted.");
        }
    }


    //////////////////////////////// Utility functions ////////////////////////////////

    /** Return an array of all squares in the intersection of these rows and cols **/
    int[] cross(int[] rows, int[] cols) {
        int[] result = new int[rows.length * cols.length];
        int i = 0;
        for (int r : rows) {
            for (int c : cols) {
                result[i++] = N * r + c;
            }
        }
        return result;
    }

    /** Return true iff item is an element of array. **/
    boolean member(int item, int[] array) { return member(item, array, array.length); }

    /** Return true iff item appears within array[0..end). **/
    boolean member(int item, int[] array, int end) {
        for (int i = 0; i < end; ++i) {
            if (array[i] == item) return true;
        }
        return false;
    }


    //////////////////////////////// Constants ////////////////////////////////

    final int     N          = 9;
    final int[]   DIGITS     = {1<<0, 1<<1, 1<<2, 1<<3, 1<<4, 1<<5, 1<<6, 1<<7, 1<<8};
    final int     ALL_DIGITS = Integer.parseInt("111111111", 2);
    final int[]   ROWS       = IntStream.range(0, N).toArray();
    final int[]   COLS       = ROWS;
    final int[]   SQUARES    = IntStream.range(0, N * N).toArray();
    final int[][] BLOCKS     = {{0,1,2},{3,4,5},{6,7,8}};
    final int[][] ALL_UNITS  = new int[3 * N][];
    final int[][][] UNITS    = new int[N * N][3][N];
    final int[][] PEERS      = new int[N * N][20];
    final int[]   NUM_DIGITS      = new int[ALL_DIGITS + 1];
    final int[]   HIGHEST_DIGIT   = new int[ALL_DIGITS + 1];

    {
        int i = 0;
        for (int r : ROWS)   { ALL_UNITS[i++] = cross(new int[]{r}, COLS); }
        for (int c : COLS)   { ALL_UNITS[i++] = cross(ROWS, new int[]{c}); }
        for (int[] rb : BLOCKS) {
            for (int[] cb : BLOCKS) { ALL_UNITS[i++] = cross(rb, cb); }
        }

        for (int s : SQUARES) {
            i = 0;
            for (int[] u : ALL_UNITS) {
                if (member(s, u)) UNITS[s][i++] = u;
            }
        }

        for (int s : SQUARES) {
            i = 0;
            for (int[] u : UNITS[s]) {
                for (int s2 : u) {
                    if (s2 != s && !member(s2, PEERS[s], i)) {
                        PEERS[s][i++] = s2;
                    }
                }
            }
        }

        for (int val = 0; val <= ALL_DIGITS; val++) {
            NUM_DIGITS[val]    = Integer.bitCount(val);
            HIGHEST_DIGIT[val] = Integer.highestOneBit(val);
        }
    }


    //////////////////////////////// Search algorithm ////////////////////////////////

    /** Search for a solution to grid. If there is an unfilled square, select one
     ** and try--that is, search recursively--every possible digit for the square. **/
    int[] search(int[] grid, int[][] gridpool, int level) {
        if (grid == null) return null;
        int s = select_square(grid);
        if (s == -1) return grid; // All squares filled — puzzle is solved.
        for (int d : DIGITS) {
            if ((d & grid[s]) > 0) {
                System.arraycopy(grid, 0, gridpool[level], 0, grid.length);
                int[] result = search(fill(gridpool[level], s, d), gridpool, level + 1);
                if (result != null) return result;
                backtracks.incrementAndGet(); // thread-safe 
            }
        }
        return null;
    }


    /** Verify that grid is a valid solution to puzzle. **/
    boolean verify(int[] grid, int[] puzzle) {
        if (grid == null) return false;
        for (int s : SQUARES) {
            if (NUM_DIGITS[grid[s]] != 1
                    || (NUM_DIGITS[puzzle[s]] == 1 && grid[s] != puzzle[s])) {
                return false;
            }
        }
        for (int[] u : ALL_UNITS) {
            int unitDigits = 0;
            for (int s : u) { unitDigits |= grid[s]; }
            if (unitDigits != ALL_DIGITS) return false;
        }
        return true;
    }


    /** Choose the unfilled square with the fewest possible values.
     ** Return -1 if all squares are filled (puzzle complete). **/
    int select_square(int[] grid) {
        int square = -1;
        int min = N + 1;
        for (int s : SQUARES) {
            int c = NUM_DIGITS[grid[s]];
            if (c == 2) return s;       // Can't do better than 2
            if (c > 1 && c < min) {
                square = s;
                min = c;
            }
        }
        return square;
    }


    /** Fill grid[s] = d. Return null if this creates a contradiction. **/
    int[] fill(int[] grid, int s, int d) {
        if (grid == null || (grid[s] & d) == 0) return null;
        grid[s] = d;
        for (int p : PEERS[s]) {
            if (!eliminate(grid, p, d)) return null;
        }
        return grid;
    }


    /** Eliminate digit d as a possibility for grid[s].
     ** Run all three constraint-propagation routines.
     ** Return false if a contradiction is detected. **/
    boolean eliminate(int[] grid, int s, int d) {
        if ((grid[s] & d) == 0) return true; // Already eliminated
        grid[s] -= d;
        return arc_consistent(grid, s) && dual_consistent(grid, s, d) && naked_pairs(grid, s);
    }


    //////////////////////////////// Constraint Propagation ////////////////////////////////

    /** Check arc consistency: either s has multiple possibilities, or its single
     ** remaining value can be filled without contradiction. **/
    boolean arc_consistent(int[] grid, int s) {
        int count = NUM_DIGITS[grid[s]];
        return count >= 2 || (count == 1 && fill(grid, s, grid[s]) != null);
    }


    /** After eliminating d from grid[s], ensure d still has at least one valid
     ** position in each of s's units. If exactly one remains, fill it. **/
    boolean dual_consistent(int[] grid, int s, int d) {
        for (int[] u : UNITS[s]) {
            int dPlaces = 0;
            int dPlace  = -1;
            for (int s2 : u) {
                if ((grid[s2] & d) > 0) {
                    if (++dPlaces > 1) break;
                    dPlace = s2;
                }
            }
            if (dPlaces == 0 || (dPlaces == 1 && fill(grid, dPlace, d) == null)) {
                return false;
            }
        }
        return true;
    }


    /** If two squares in a unit share exactly the same two possible values, eliminate
     ** those values from every other square in that unit (naked pairs strategy). **/
    boolean naked_pairs(int[] grid, int s) {
        if (!runNakedPairs || NUM_DIGITS[grid[s]] != 2) return true;
        int val = grid[s];
        for (int s2 : PEERS[s]) {
            if (grid[s2] == val) {
                for (int[] u : UNITS[s]) {
                    if (member(s2, u)) {
                        int d  = HIGHEST_DIGIT[val];
                        int d2 = val - d;
                        for (int s3 : u) {
                            if (s3 != s && s3 != s2) {
                                if (!eliminate(grid, s3, d) || !eliminate(grid, s3, d2)) {
                                    return false;
                                }
                            }
                        }
                    }
                }
            }
        }
        return true;
    }


    //////////////////////////////// Input ////////////////////////////////

    /** Read one puzzle per line from filename and return a list of puzzle grids. **/
    List<int[]> readPuzzlesFromFile(String filename) throws IOException {
        try (BufferedReader in = new BufferedReader(new FileReader(filename))) {
            List<int[]> grids = new ArrayList<>(1000);
            String gridstring;
            while ((gridstring = in.readLine()) != null) {
                grids.add(parseGrid(gridstring));
                if (reversePuzzle) {
                    grids.add(parseGrid(new StringBuilder(gridstring).reverse().toString()));
                }
            }
            return grids;
        }
    }


    /** Parse a gridstring into a puzzle grid. **/
    int[] parseGrid(String gridstring) {
        int[] grid = new int[N * N];
        int s = 0;
        for (int i = 0; i < gridstring.length(); ++i) {
            char c = gridstring.charAt(i);
            if ('1' <= c && c <= '9') {
                grid[s++] = DIGITS[c - '1'];
            } else if (c == '0' || c == '.') {
                grid[s++] = ALL_DIGITS;
            }
        }
        if (s != N * N) {
            throw new IllegalArgumentException(
                "Grid string yielded " + s + " squares; expected " + (N * N) + ": \"" + gridstring + "\"");
        }
        return grid;
    }


    /** Initialize a fresh grid from puzzle, then fill known squares to trigger constraint propagation. **/
    int[] initialize(int[] puzzle) {
        int[] grid = new int[N * N];
        Arrays.fill(grid, ALL_DIGITS);
        for (int s : SQUARES) {
            if (puzzle[s] != ALL_DIGITS) fill(grid, s, puzzle[s]);
        }
        return grid;
    }


    //////////////////////////////// Output and Tests ////////////////////////////////

    /** Print stats: puzzles solved, average µs, KHz, threads, backtracks, and name. **/
    void printStats(int nGrids, long startTime, String name) {
        double usecs = (System.nanoTime() - startTime) / 1_000.0;
        int bt = backtracks.getAndSet(0); // thread-safe
        String line = String.format("%7d %6.1f %7.3f %7d %10.1f %s",
            nGrids, usecs / nGrids, 1_000 * nGrids / usecs, nThreads, bt * 1.0 / nGrids, name);
        synchronized (this) {
            if (!headerPrinted) {
                System.out.println("Puzzles   μsec     KHz Threads Backtracks Name\n"
                                 + "======= ====== ======= ======= ========== ====");
                headerPrinted = true;
            }
            System.out.println(line);
        }
    }


    /** Print the original puzzle grid alongside the solution grid. **/
    void printGrids(String name, int[] puzzle, int[] solution) {
        final String BAR = "------+-------+------";
        final String GAP = "      ";
        if (solution == null) solution = new int[N * N];
        synchronized (this) {
            System.out.format("\n%-22s%s%s\n", name + ":", GAP,
                verify(solution, puzzle) ? "Solution:" : "FAILED:");
            for (int r = 0; r < N; ++r) {
                System.out.println(rowString(puzzle, r) + GAP + rowString(solution, r));
                if (r == 2 || r == 5) System.out.println(BAR + GAP + " " + BAR);
            }
        }
    }


    /** Return a String representing one row of the grid. **/
    String rowString(int[] grid, int r) {
        StringBuilder row = new StringBuilder(30);
        for (int s = r * 9; s < (r + 1) * 9; ++s) {
            int nd = NUM_DIGITS[grid[s]];
            char cell = nd == 9 ? '.' : nd != 1 ? '?' : (char)('1' + Integer.numberOfTrailingZeros(grid[s]));
            row.append(cell);
            row.append(s % 9 == 2 || s % 9 == 5 ? " | " : " ");
        }
        return row.toString();
    }


    /** Unit Tests. **/
    void runUnitTests() {
        assert N == 9;
        assert SQUARES.length == 81;
        for (int s : SQUARES) {
            assert UNITS[s].length == 3;
            assert PEERS[s].length == 20;
        }
        assert Arrays.equals(PEERS[19],
            new int[]{18,20,21,22,23,24,25,26,1,10,28,37,46,55,64,73,0,2,9,11});
        assert Arrays.deepToString(UNITS[19]).equals(
            "[[18, 19, 20, 21, 22, 23, 24, 25, 26], [1, 10, 19, 28, 37, 46, 55, 64, 73], [0, 1, 2, 9, 10, 11, 18, 19, 20]]");
        System.out.println("Unit tests pass.");
    }
}